


"""simple docstring"""



from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload







class    __a						:







				def __init__( self      ,	UpperCAmelCase = None   ):

					'''simple docstring'''






					if components is None:
						lowerCAmelCase_      							=			[]
					lowerCAmelCase_      							=			list(UpperCAmelCase   )







				def __len__( self   ):

					'''simple docstring'''






					return len(self.__components   )







				def __str__( self   ):

					'''simple docstring'''






					return "(" + ",".join(map(UpperCAmelCase      ,	self.__components   )   ) + ")"







				def __add__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					lowerCAmelCase_      							=			len(self   )
					if size == len(UpperCAmelCase   ):
						lowerCAmelCase_      							=			[self.__components[i] + other.component(UpperCAmelCase   ) for i in range(UpperCAmelCase   )]
						return Vector(UpperCAmelCase   )
					else:
						raise Exception('''must have the same size'''   )







				def __sub__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					lowerCAmelCase_      							=			len(self   )
					if size == len(UpperCAmelCase   ):
						lowerCAmelCase_      							=			[self.__components[i] - other.component(UpperCAmelCase   ) for i in range(UpperCAmelCase   )]
						return Vector(UpperCAmelCase   )
					else:  # error case
						raise Exception('''must have the same size'''   )







				@overload
				def __mul__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					...







				@overload
				def __mul__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					...







				def __mul__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if isinstance(UpperCAmelCase      ,	(float, int)   ):
						lowerCAmelCase_      							=			[c * other for c in self.__components]
						return Vector(UpperCAmelCase   )
					elif isinstance(UpperCAmelCase      ,	UpperCAmelCase   ) and len(self   ) == len(UpperCAmelCase   ):
						lowerCAmelCase_      							=			len(self   )
						lowerCAmelCase_      							=			[self.__components[i] * other.component(UpperCAmelCase   ) for i in range(UpperCAmelCase   )]
						return sum(UpperCAmelCase   )
					else:  # error case
						raise Exception('''invalid operand!'''   )







				def      lowerCamelCase_     ( self   ):

					'''simple docstring'''






					return Vector(self.__components   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if isinstance(UpperCAmelCase      ,	UpperCAmelCase   ) and -len(self.__components   ) <= i < len(self.__components   ):
						return self.__components[i]
					else:
						raise Exception('''index out of range'''   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					assert -len(self.__components   ) <= pos < len(self.__components   )
					lowerCAmelCase_      							=			value







				def      lowerCamelCase_     ( self   ):

					'''simple docstring'''






					if len(self.__components   ) == 0:
						raise Exception('''Vector is empty'''   )
					lowerCAmelCase_      							=			[c**2 for c in self.__components]
					return math.sqrt(sum(UpperCAmelCase   )   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase = False   ):

					'''simple docstring'''






					lowerCAmelCase_      							=			self * other
					lowerCAmelCase_      							=			self.euclidean_length() * other.euclidean_length()
					if deg:
						return math.degrees(math.acos(num / den   )   )
					else:
						return math.acos(num / den   )




def      UpperCAmelCase     (       _lowercase :   int	)						-> Vector:


	"""simple docstring"""




	assert isinstance(_lowercase			,   _lowercase	)
	return Vector([0] * dimension	)
def      UpperCAmelCase     (       _lowercase :   int			,   _lowercase :   int	)						-> Vector:


	"""simple docstring"""




	assert isinstance(_lowercase			,   _lowercase	) and (isinstance(_lowercase			,   _lowercase	))
	lowerCAmelCase_      							=			[0] * dimension
	lowerCAmelCase_      							=			1
	return Vector(_lowercase	)
def      UpperCAmelCase     (       _lowercase :   float			,   _lowercase :   Vector			,   _lowercase :   Vector	)						-> Vector:


	"""simple docstring"""




	assert (
	    isinstance(_lowercase			,   _lowercase	)
	    and isinstance(_lowercase			,   _lowercase	)
	    and (isinstance(_lowercase			,   (int, float)	))
	)
	return x * scalar + y
def      UpperCAmelCase     (       _lowercase :   int			,   _lowercase :   int			,   _lowercase :   int	)						-> Vector:


	"""simple docstring"""




	random.seed(_lowercase	)
	lowerCAmelCase_      							=			[random.randint(_lowercase			,   _lowercase	) for _ in range(_lowercase	)]
	return Vector(_lowercase	)







class    __a						:







				def __init__( self      ,	UpperCAmelCase      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					lowerCAmelCase_      							=			matrix
					lowerCAmelCase_      							=			w
					lowerCAmelCase_      							=			h







				def __str__( self   ):

					'''simple docstring'''






					lowerCAmelCase_      							=			''''''
					for i in range(self.__height   ):
						ans += "|"
						for j in range(self.__width   ):
							if j < self.__width - 1:
								ans += str(self.__matrix[i][j]   ) + ","
							else:
								ans += str(self.__matrix[i][j]   ) + "|\n"
					return ans







				def __add__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if self.__width == other.width() and self.__height == other.height():
						lowerCAmelCase_      							=			[]
						for i in range(self.__height   ):
							lowerCAmelCase_      							=			[
							    self.__matrix[i][j] + other.component(UpperCAmelCase      ,	UpperCAmelCase   )
							    for j in range(self.__width   )
							]
							matrix.append(UpperCAmelCase   )
						return Matrix(UpperCAmelCase      ,	self.__width      ,	self.__height   )
					else:
						raise Exception('''matrix must have the same dimension!'''   )







				def __sub__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if self.__width == other.width() and self.__height == other.height():
						lowerCAmelCase_      							=			[]
						for i in range(self.__height   ):
							lowerCAmelCase_      							=			[
							    self.__matrix[i][j] - other.component(UpperCAmelCase      ,	UpperCAmelCase   )
							    for j in range(self.__width   )
							]
							matrix.append(UpperCAmelCase   )
						return Matrix(UpperCAmelCase      ,	self.__width      ,	self.__height   )
					else:
						raise Exception('''matrices must have the same dimension!'''   )







				@overload
				def __mul__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					...







				@overload
				def __mul__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					...







				def __mul__( self      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if isinstance(UpperCAmelCase      ,	UpperCAmelCase   ):  # matrix-vector
						if len(UpperCAmelCase   ) == self.__width:
							lowerCAmelCase_      							=			zero_vector(self.__height   )
							for i in range(self.__height   ):
								lowerCAmelCase_      							=			[
								    self.__matrix[i][j] * other.component(UpperCAmelCase   )
								    for j in range(self.__width   )
								]
								ans.change_component(UpperCAmelCase      ,	sum(UpperCAmelCase   )   )
							return ans
						else:
							raise Exception(
							    '''vector must have the same size as the '''
							    '''number of columns of the matrix!'''   )
					elif isinstance(UpperCAmelCase      ,	(int, float)   ):  # matrix-scalar
						lowerCAmelCase_      							=			[
						    [self.__matrix[i][j] * other for j in range(self.__width   )]
						    for i in range(self.__height   )
						]
						return Matrix(UpperCAmelCase      ,	self.__width      ,	self.__height   )
					return None







				def      lowerCamelCase_     ( self   ):

					'''simple docstring'''






					return self.__height







				def      lowerCamelCase_     ( self   ):

					'''simple docstring'''






					return self.__width







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if 0 <= x < self.__height and 0 <= y < self.__width:
						return self.__matrix[x][y]
					else:
						raise Exception('''change_component: indices out of bounds'''   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if 0 <= x < self.__height and 0 <= y < self.__width:
						lowerCAmelCase_      							=			value
					else:
						raise Exception('''change_component: indices out of bounds'''   )







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if self.__height != self.__width:
						raise Exception('''Matrix is not square'''   )
					lowerCAmelCase_      							=			self.__matrix[:x] + self.__matrix[x + 1 :]
					for i in range(len(UpperCAmelCase   )   ):
						lowerCAmelCase_      							=			minor[i][:y] + minor[i][y + 1 :]
					return Matrix(UpperCAmelCase      ,	self.__width - 1      ,	self.__height - 1   ).determinant()







				def      lowerCamelCase_     ( self      ,	UpperCAmelCase      ,	UpperCAmelCase   ):

					'''simple docstring'''






					if self.__height != self.__width:
						raise Exception('''Matrix is not square'''   )
					if 0 <= x < self.__height and 0 <= y < self.__width:
						return (-1) ** (x + y) * self.minor(UpperCAmelCase      ,	UpperCAmelCase   )
					else:
						raise Exception('''Indices out of bounds'''   )







				def      lowerCamelCase_     ( self   ):

					'''simple docstring'''






					if self.__height != self.__width:
						raise Exception('''Matrix is not square'''   )
					if self.__height < 1:
						raise Exception('''Matrix has no element'''   )
					elif self.__height == 1:
						return self.__matrix[0][0]
					elif self.__height == 2:
						return (
						    self.__matrix[0][0] * self.__matrix[1][1]
						    - self.__matrix[0][1] * self.__matrix[1][0]
						)
					else:
						lowerCAmelCase_      							=			[
						    self.__matrix[0][y] * self.cofactor(0      ,	UpperCAmelCase   ) for y in range(self.__width   )
						]
						return sum(UpperCAmelCase   )




def      UpperCAmelCase     (       _lowercase :   int	)						-> Matrix:


	"""simple docstring"""




	lowerCAmelCase_      							=			[[0] * n for _ in range(_lowercase	)]
	return Matrix(_lowercase			,   _lowercase			,   _lowercase	)





def      UpperCAmelCase     (       _lowercase :   int			,   _lowercase :   int			,   _lowercase :   int			,   _lowercase :   int	)						-> Matrix:


	"""simple docstring"""




	random.seed(_lowercase	)
	lowerCAmelCase_      							=			[
	    [random.randint(_lowercase			,   _lowercase	) for _ in range(_lowercase	)] for _ in range(_lowercase	)
	]
	return Matrix(_lowercase			,   _lowercase			,   _lowercase	)



"""simple docstring"""



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tokenizers_available,
    is_torch_available,
    is_vision_available,
)


lowercase_							=							{
    'configuration_layoutlmv2': ['LAYOUTLMV2_PRETRAINED_CONFIG_ARCHIVE_MAP', 'LayoutLMv2Config'],
    'processing_layoutlmv2': ['LayoutLMv2Processor'],
    'tokenization_layoutlmv2': ['LayoutLMv2Tokenizer'],
}

try:
		if not is_tokenizers_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowercase_							=							['LayoutLMv2TokenizerFast']

try:
		if not is_vision_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowercase_							=							['LayoutLMv2FeatureExtractor']
		lowercase_							=							['LayoutLMv2ImageProcessor']

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowercase_							=							[
		    'LAYOUTLMV2_PRETRAINED_MODEL_ARCHIVE_LIST',
		    'LayoutLMv2ForQuestionAnswering',
		    'LayoutLMv2ForSequenceClassification',
		    'LayoutLMv2ForTokenClassification',
		    'LayoutLMv2Layer',
		    'LayoutLMv2Model',
		    'LayoutLMv2PreTrainedModel',
		]

if TYPE_CHECKING:
		from .configuration_layoutlmva import LAYOUTLMV2_PRETRAINED_CONFIG_ARCHIVE_MAP, LayoutLMvaConfig
		from .processing_layoutlmva import LayoutLMvaProcessor
		from .tokenization_layoutlmva import LayoutLMvaTokenizer

		try:
				if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_layoutlmva_fast import LayoutLMvaTokenizerFast

		try:
				if not is_vision_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .feature_extraction_layoutlmva import LayoutLMvaFeatureExtractor, LayoutLMvaImageProcessor

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_layoutlmva import (
				    LAYOUTLMV2_PRETRAINED_MODEL_ARCHIVE_LIST,
				    LayoutLMvaForQuestionAnswering,
				    LayoutLMvaForSequenceClassification,
				    LayoutLMvaForTokenClassification,
				    LayoutLMvaLayer,
				    LayoutLMvaModel,
				    LayoutLMvaPreTrainedModel,
				)
else:
		import sys

		lowercase_							=							_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)